Which system of linear inequalities has the point 2 1

Posted By Admin @ November 26, 2022

Question:

Which system of linear inequalities has the point (2 ,1) in its solution set?

Answer:

Answer:

The system of Linear equation is x + 2y ≤ 4 and 2x - y > 0

Step-by-step explanation:

Given: Point ( 2 , 1 )

To find: System of Linear Inequalities which contain given point in

              its solution set

There are 2 lines passing through point ( 2 , 1 )

So first we find the equation of both lines

Equation of line using Two-Point form is given by,

(y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)

Equation of line 1 passing through ( 0 , 2 ) & ( 4 , 0 )

(y-2)=\frac{0-2}{4-0}(x-0)

(y-2)=\frac{-2}{4}x

(y-2)=\frac{-x}{2}

y=\frac{-x}{2}+2

y+\frac{x}{2}=2

x+2y=4 ....... (1)

Equation line 2 passing through ( 0 , 0 )  & ( 2 , 1 )

(y-0)=\frac{0-2}{0-1}(x-0)

y=\frac{-2}{-1}x

y=2x

2x-y=0 ....... (2)

Now from given graph is clear line 1 contain the given point and area shaded by it is toward origin then we have less than equal sign,

⇒ x + 2y ≤ 4

Line 2 is dotted line. So, it does not contain the given point and area shaded by it is toward 4th quadrant then we have greater than sign in it.

⇒ 2x - y > 0

Therefore, The system of Linear equation is x + 2y ≤ 4 and 2x - y > 0

Similar Questions

  1. Which system of linear inequalities is represented by the graph
  2. Write a system of linear inequalities represented by the graph
  3. Write a system of linear inequalities represented by the graph.
  4. Name three or more different methods for solving linear systems.
  5. 2 1 3 divided by 7 3 8 in fraction
  6. 2 1 2 x 3 4 2x 5 3 8
  7. 1 2 to the power of 3 in fraction form
  8. 1 2 to the power of 4 in fraction form
  9. 1 1 2 sticks of butter equals how many cups
  10. 1 1 2 divided by 3 4 as a fraction
  11. 1 2 to the power of 4 as a fraction
  12. 1 2 to the power of 6 as a fraction
  13. 1 1 2 2 3 3 4 4 5 5
  14. 1 2 to the power of 5 as a fraction
  15. 1 2 to the power of 3 as a fraction
  16. 1 2 3 4 5 6 7 8 9 9
  17. 1 1 2 cups of butter is how many sticks
  18. 1 1 2 sticks of butter equals how many tablespoons
  19. 2 1 5 divided by 2 1 4 simplest form
  20. 2 2 is 4 minus 1 thats 3 quick maths
  21. 5 1 2 percent as a fraction in simplest form
  22. Block 1 is resting on the floor with block 2
  23. Act 1 scene 2 a raisin in the sun quizlet
  24. Block 1 of mass m1 is placed on block 2
  25. Unit 5 test systems of equations & inequalities answer key
  26. 1 2 3 x 2 1 2 as a fraction
  27. 2 3 4 1 4 5 as a mixed number
  28. 37x 1 2 x 1 4 9 4x 7 5
  29. 1 8 to the power of 2 as a fraction
  30. 1 4 to the power of 2 as a fraction
  31. 1 5 to the power of 2 as a fraction
  32. 1 less than the product of 2 and a number
  33. 1 1 2 3 5 8 13 21 34 55
  34. 1 3 2 3 3 3 4 3 5 3
  35. 1 3 to the power of 2 as a fraction
  36. 1 3 7 divided by 2 3 as a fraction
  37. 1 3 5 divided by 2 3 as a fraction
  38. Points lines and planes worksheet answers unit 1 lesson 1
  39. 3 3 4 2 1 5 as a mixed number
  40. 1 2 3 5 8 13 21 34 55 89
  41. 4 1 6 2 3 4 as a mixed number
  42. 0 1 1 2 3 5 8 13 21 34
  43. Articles 1 2 and 3 of the constitution describe the
  44. 0 1 1 2 3 5 8 13 34 55
  45. 4 2 3 divided by 1 2 as a fraction
  46. 2 3 1 4x 2 1 5 4 3x 1
  47. 3 3 4 divided by 2 1 12 in fraction
  48. 1 3 6x 5 x 1 3 2 x 1
  49. Freeze columns a and b and rows 1 and 2
  50. 5 1 2 divided by 3 4 in fraction form
  51. 1 2 4 8 16 32 64 128 256 512
  52. 3x 2 2x 7 0 then x 1 3 2
  53. 1 2/3 x 2 1/3 x 2 as a fraction
  54. 3 4 1 3 divided by 1 6 1 2
  55. Kuta software infinite algebra 1 finding slope from two points
  56. Caroline bought 20 shares of stock at 10 1 2
  57. 6 1 2 7 8 divided by 5 11 16
  58. 2x y 10 y 1 solve the system of equations
  59. Schister systems uses the following data in its cost-volume-profit analysis
  60. Schister systems uses the following data in its cost-volume-profit analyses
  61. Which linear inequality is represented by the graph y 1/3x-4
  62. Preganglionic neurons of the autonomic nervous system are located in
  63. Linear relations are not functions when they appear graphically as
  64. A system of linear equations with more equations than unknowns
  65. Which linear inequality is represented by the graph y 2/3x-1/5
  66. Three points on a plane always form a triangle counterexample
  67. Historians label an event as a turning point when it
  68. Signal propagation in the nervous system can be modeled as
  69. Which linear inequality is represented by the graph y 1/2x+2
  70. Line passes through the point and has a slope of
  71. Which linear inequality is represented by the graph y 2/3x+3
  72. Five sided yellow sign with a point at the top
  73. Select the correct answer. graph the following system of inequalities.
  74. Straight path of points that continues in two opposite directions
  75. Elise jake malik and xiao each solved the same inequality

Paleocene organisms that may have been the first primates were

Plesiadapiforms are organisms that may have been the first primates. This group of primates underwent an adaptive radiation which enable them to produce forms with …

A random blood sugar reading that falls between 70-110 mg/dl

Answer:Truethere's a bunch of quizlets with the answer

What state of matter has no definite shape or volume

Answer:A. Liquid .Explanation:Hello there!In this case, according to the given information, it turns possible for us to to infer that the answer is A. Liquid …

Southerners reacted to the raid at harpers ferry by ______.

Answer:The following events best describe after the failed rebellion at Harper's Ferry:A-Abraham Lincoln and Stephen Douglas condemned the violenceB-more and more Southerners saw leaving the …

According to hubble's law the greater a galaxy's redshift the

The question about the finding the true statement based on the space.Hubble's law is based on the observed physical cosmology and the galaxy that are …

What was a provision of the usa patriot act brainly

"The government could eavesdrop on telephone calls and privileged conversations between prisoners and their lawyers" and "The government could violate due process laws if a …

Being tired has very similar effects on the body as

The correct answer is AlcoholYour body reaction time when tired is quite similar to body reaction time while intoxicated.

A parallelogram with four equal sides but no right angles

Answer:parallelogramrhombuskiteExplanation:A shape that has four sides is generally known as quadrilateral.Quadrilaterals can be:1- parallelogram: this one has no right angles. Therefore, it is a correct …

The maximum fine for a first non driving alcohol related

Heavy amphetamine use: makes a driver less coordinated and at times more likely to be involved in an accident If a minor under the age …

A ____________ is an abnormal elevation of the body temperature.

A fever is an abnormal elevation of the body temperature. A low to moderate fever, when a low to moderate fever, when allowed to run …

All of the following are benefits of physical activity except

Wouldn’t the answer be risk of injury

Which of the following statements about diabetes is not true:

Hello lobe the answer is c

The phrase the middle of may is an example of

The phrase "middle of May" is an example of an alliteration. The correct answer is option A. Alliteration is a literary device that uses the …

A pound of body fat contains approximately how many calories

It has been proven that the caloric equivalent of one pound of body fat is 3500 calories approximately. One pound is equal to 454 grams …

Create a following distance greater than 3 seconds ahead when

Answer:option (a)Explanation:Maintaining distance while driving in traffic can avoid the chances of an accident. When the driver is behind you is trying to pass you …